L'Hospital rule?

Question

x Tan(9/x)
Lim x-> infinity
I know it would be tan(9/x)/(1/x) or x/(1/tan(9/x) but I am not sure which one to use help please

Answer 1

Either one's technically correct, but the one worth using is tan (9/x)/(1/x). The other one just produces a mess. Thus:

[x→∞]lim tan (9/x)/(1/x)
[x→∞]lim sec² (9/x) * (-9/x²)/(-1/x²)
9 [x→∞]lim sec² (9/x)
9 sec² 0
9